2.1 Understanding and predicting seasonal tropical SST variations

CDC scientists have pioneered the development of Linear Inverse
Modeling (LIM) as a diagnostic and forecasting tool. LIM is a method
of extracting the dynamical parameters of a system from data. The
assumption is made that the dynamics can be modeled as a stable linear
multivariate process driven by geographically coherent white
noise. The estimated dynamical parameters can then be used to make
forecasts of the system. Real-time seasonal LIM forecasts of tropical
Indo-Pacific SST anomalies are published monthly in the Climate
Diagnostics Bulletin and quarterly in the Experimental
Long-Lead Forecast Bulletin (ELLFB). They are also available
through CDC's website at http://www.esrl.noaa.gov/psd/~lem/IndoPacific.frcst.html.

An important original result from our LIM diagnosis of Indo-Pacific
SST variability was the identification, through a singular-vector
analysis of the empirically-determined system propagator, of an
optimal initial SST pattern for SST anomaly growth over 7 months in
the basin. This structure evolves in 7 months into a pattern
resembling a mature ENSO event (Fig. 2.1), and
may therefore be viewed as a dynamically relevant precursor to ENSO.

Fig. 2.1 (a) The optimal initial structure for
SST anomaly growth. The pattern is normalized to unity. The contour
interval is 0.025. Loadings greater than 0.025 are colored red; dashed
lines indicate negative contours. (b) The pattern predicted when the
pattern in (a) is used as the initial condition.

And indeed, as Fig. 2.2. shows, whenever an
SST anomaly pattern projects appreciably on this structure, there is a
good chance of obtaining large SST anomalies in the Niño 3.4 area 7
months later. Figure 2.2 also shows that the
projection statistics are similar whether they are evaluated for a
time period including the training period (COADS data: 1950-1990) or
for independent data (NMC Real-time Surface Marine data:
1991-2001). Encouraged by this robust behavior, we now provide
real-time monitoring of the projection of the SST anomaly field on
this structure through our website at http://www.esrl.noaa.gov/psd/~lem/opt/optstr.html.

Fig. 2.2 Left panels: Time series of SST anomaly
in Niño 3.4 (blue line), and the pattern correlation of the SST
anomaly pattern seven months earlier with the optimal structure (red
line). The information in these left panels is also displayed in the
form of scatter plots in the right panels.

We have also recently published procedures for estimating improved
confidence intervals on our SST forecasts. Until recently, the
confidence intervals were those appropriate to our assumed stationary
linear Markov process; that is, they showed the expected forecast
error of a stable linear model driven by stationary white noise. The
improved error bars also include estimated contributions from our
neglect of the seasonal variation of the stochastic forcing, from
estimating the model's parameters in a training period of finite
length, and from initial condition errors.

The actual forecast error normalized by the rms of the total expected
error estimated in this manner (Fig. 2.3) shows
how much better the forecast skill is during La Niña than El
Niño. This is consistent with our conclusion, stated in several
papers, that nonlinear dynamics become important during the warmest
phase of warm events. We have continued to investigate the failure of
LIM during such periods. Although the lack of skill is mostly due to
the greater importance of nonlinearity, an interesting recent finding
was that LIM would nevertheless have been useful during late
1994-early 1995 had it been applied to weekly instead of seasonal
SSTs. Evidence has also been found that unpredictable stochastic
forcing accounted for a large portion of the observed warming during
the strong 1997-1998 event.

Fig. 2.3 Time series of actual LIM forecast
errors normalized by one standard deviation of the total forecast
uncertainty. The horizontal lines at +/- 1.96 indicate the 95%
confidence interval. The red and blue arrows indicate prominent El
Niño and La Niña events during this period.

CDC also provides LIM forecasts of the tropical north Atlantic and
Caribbean SSTs in the ELLFB. Again, these forecasts are available
through our website at http://www.esrl.noaa.gov/psd/~lem/Atlantic.forecast.html. We
have shown that forecast skill in these Atlantic regions is related to
the skill of predicting El Niño. We have also used LIM to diagnose the
dynamical nature of tropical Atlantic SST variability, and published
evidence that the familiar "dipole" SST anomaly pattern is a
dynamically realizable structure (as opposed to merely the dominant
EOF of regional SST variability), but whose development is often
interrupted by ENSO influences from the east Pacific.

Our original claim that the basic dynamics of ENSO are stable, linear
and stochastically forced has been independently confirmed by others
and is gradually forcing a paradigm shift in this field. We have
continued investigating the dynamical nature of ENSO, especially in
collaboration with scientists at Texas A&M University. A recently
published study showed that an intermediate coupled ENSO-prediction
model of the Cane-Zebiak type, tuned to be in a stable stochastically
forced regime, generated more realistic SST variability than did the
same model tuned to give self-sustained oscillations.